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Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions. (English) Zbl 1103.65302
Summary: A general procedure is derived for simulating univariate and multivariate nonnormal distributions using polynomial transformations of order five. The procedure allows for the additional control of the fifth and sixth moments. The ability to control higher moments increases the precision in the approximations of nonnormal distributions and lowers the skew and kurtosis boundary relative to the competing procedures considered. Tabled values of constants are provided for approximating various probability density functions. A numerical example is worked to demonstrate the multivariate procedure. The results of a Monte Carlo simulation are provided to demonstrate that the procedure generates specified population parameters and intercorrelations.
MSC:
65C10Random number generation (numerical analysis)
65C60Computational problems in statistics
65C05Monte Carlo methods
62E99Statistical distribution theory